The multinomial logit approach employs utility functions and maintains the ordinal nature associ-
ated with economic utility theory. Thus, the model is based on shares of effort in the activities,
but returns and risks are classified in terms of utility. This utility is not directly convertible to
income or monetary units. However, changes in the utility received by households over time can
be tracked. Accordingly, the model in Fig. 1 shows a sub-model the household utility sector
that totals the sectors’ returns and records their flows over time. These amounts may also be
accumulated and discounted to compare net present values of alternative scenarios.
It could be possible to identify the parameters on each element of the utility functions through a
detailed econometric analysis of the shares that households invest in these activities and the re-
turns and risks they face. In a simple financial analysis the household would ‘invest’ resources to
the point where the marginal returns from these activities are equated between sectors and periods
over time. However, several activities that com- munal households expend effort on do not have
market values. For example, collection of non- wood products from the communal forest is a
significant
household activity,
especially in
drought years, but attempts to value these prod- ucts in conventional economic terms have been
difficult. Furthermore, given the limited role of cash in the communal economies of the region,
strictly using returns in monetary units would probably not accurately reflect the value of these
resources to the household. Accordingly, data for econometric estimations of return functions from
the various sectors are not available. The ap- proach taken in this paper was to construct a
simple model by calibrating the parameters on the variables affecting utilities, according to knowl-
edge about the local community and their re- sponses to changes in rainfall, and population
numbers.
4. Model calibration
In order to calibrate the model, known infor- mation regarding returns received, effort allo-
cated, risks, population, rainfall, and biomass were collected.
4
.
1
. Returns and effort A study in Chivi communal area Natural re-
gion IV found the following sources of wealth: crops 33, remittances 13, off-farm income
48 and livestock income 7 GFA, 1987. By contrast, in Chilimanzi, crop sales represent 50
of income, livestock products 6, urban remit- tances 13 and off-farm income 32 Steinfeld,
1988. For the purposes of our study, we also need information about percentages of household
income derived from sectors, such as non-wood woodland products, that do not necessarily have
market values.
9
For this reason we chose to use data presented by Cavendish 1997, which come
from Shindi Ward in Southern Zimbabwe.
10
The
Fig. 2. Household income cash and in-kind by sector.
9
While we are aware of the great cultural importance of some woodland localities for traditional religious purposes
such as rainmaking ceremonies e.g. Hot Springs Working Group, 1995, we have not included non-use values in calibrat-
ing the model.
10
Cavendish 1997 does not break down income according to the sectors that we have identified. However, personal
communications with Cavendish provided the breakdown re- quired. Five percent of the household income was found to
come from miscellaneous activities not captured by the above sectors. This 5 was allocated, proportionally according to
sector size, amongst the modelled sectors.
percent of household income from each sector is compiled in Fig. 2. Data regarding effort allo-
cated between sectors are not available. However, if we assume that households allocate effort
among activities in proportion to the returns that they receive, then the income percentages may
also be used as proxies for effort expended.
11
4
.
2
. Risk Unfortunately, there have been no explicit stud-
ies done on the risk perceptions of Zimbabwean households associated with these economic sec-
tors. Although no data are available on house- hold perceptions of risk or on how these vary
between wealthier and poorer households, the risks associated with different options are known
locally. In part, these are related to the nutrient poor, drought susceptible sandy soils in this area
and the risks this poses for crop production and pastoralists. Droughts and patchy rainfall also
pose a risk for more ephemeral gathered re- sources, particularly wild spinach and edible
caterpillars. In an economy where formal employ- ment options have historically been declining,
seeking work in urban areas may also be a risky option. Under risky circumstances, therefore,
woody gathered products are a mainstay provid- ing a resilient, risk-free backup if sustainably
used. Considering these and other attributes of the sectors, estimates by experts at the workshop
suggested the following risk factors associated with the model’s sectors, based on the number of
years in a decade in which the sector will fail to produce the average returns received in non-fail-
ure years: urban, 4; crops, 2; livestock, 1; non- wood, 0.5; and wood, 0.
4
.
3
. Population, rainfall, and biomass The human population of the Lupane district
was known to grow at 3 per year Gwaai Work- ing Group, 1997. Although the average rainfall
in the region is approximately 650 mmyear, the income data from Cavendish were collected dur-
ing 199394 in an area where rainfall was 523.5 mm. Accordingly, the model was calibrated as-
suming this rainfall amount. Standing biomass was assumed to be 30 tonnes per hectare Frost,
1996.
4
.
4
. Specification of model equations Given the above information, the equations of
the model in any given period were specified as: U
c
= a
c
+ b
c1
return crop × rainfall + b
c2
risk crop + b
c3
population 3
U
u
= a
u
+ b
u1
return urban × rainfall + b
u2
risk urban 4
U
n
= a
n
+ b
n1
return non-wood × rainfall + b
n2
risk non-wood 5
U
w
= a
w
+ b
w1
return wood × rainfall + b
w2
risk wood + b
w3
population + b
w4
biomass 6
U
l
= a
l
+ b
l1
return livestock × rainfall + b
l2
risk livestock + b
l3
population 7
where: U is utility derived from each sector; a is constant for each sector equation; b is marginal
utility associated with the variables; ‘return’ is return associated with each sector normalised
with crops = 1 superscripts: c, crop; u, urban; n, non-wood; w, wood; l, livestock; rainfall =
lnrain
t
ln650 where annual rainfall rain
t
is generated over time by the rainfall sub-model,
and 650 is the mean annual rainfall in mm; ‘risk’ is risk factor associated with each sector urban,
4; crops, 2; livestock, 1; non-wood, 0.5; and wood, 0;
population = 1 − 1450households
t
where households
t
is the total number of households in the study area at a given point in time with a
11
A maximising firm would attempt to get the same ratio of value of output per value of input in each sector. If not,
returns could be increased by re-allocating household re- sources. Problems with this assumption are considered in the
final section.
Fig. 3. Effect of rainfall and population growth on sector shares.
starting value of 1450 and forecast to increase by 3 per year; ‘biomass’ is total wood biomass per
hectare, estimated at a starting value of 30 tonnes. The model is solved to allocate shares among
sectors by employing these utility equations in Eq. 2.
4
.
5
. Sol6ing for model coefficients Given the above equations, the model was cali-
brated on a spreadsheet by searching for marginal utilities that caused the logistic function to dis-
tribute incomes, according to the data presented in Fig. 2. Because there was no a priori reason to
believe that the marginal utilities for a given variable would be different across sectors, values
were used that were constant across sectors. After marginal utilities that caused the model to ap-
proximate the actual income shares were found, finer calibration was done by adding constants.
The resulting marginal utilities and constants were: b
0.1
= 2; b
0.2
= − 0.01; b
0.3
= 1; b
w3
= 0.001; a
c,w
= 0; a
l
= 0.4; a
n
= 0.2; a
u
= 0.2.
With these parameters, the model was run over a 50-year period in the presence of rainfall varia-
tion and increasing population numbers. These simulations were assessed using knowledge of the
local communities’ response to significant rainfall shocks and changes in ecological conditions. As
will be described in the next section, the model seems to reflect local knowledge of sectoral
changes in response to the exogenous factors modelled.
5. Results
